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JEE Main & Advanced Mathematics Vector Algebra Question Bank Scaler or Dot product of two vectors and its application

  • question_answer
    If \[|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}\,\,|\,\,=4\] and the angle between a and b be \[{{120}^{o}}\], then \[|4\mathbf{a}+3\mathbf{b}|\,\,=\]

    A)             25

    B)             12

    C)             13

    D)             7

    Correct Answer: B

    Solution :

               \[|4\mathbf{a}+3\mathbf{b}|=\sqrt{(4\mathbf{a}+3\mathbf{b}).(4\mathbf{a}+3\mathbf{b})}\]                                    \[=\sqrt{16|\mathbf{a}{{|}^{2}}+9|\mathbf{b}{{|}^{2}}+24\mathbf{a}.\mathbf{b}}\]                                                    \[=\sqrt{144+144+24\times 3\times 4\times \left( \frac{-1}{2} \right)}=12.\]


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